# StackOverflow - Solved

looking for some solutions? You are welcome.

## SOLVED: Matrix Rotation Around an Arbitrary Axis Bug

Travis Pettry:

I have been attempting to get matrix rotation around an arbitrary axis working, I think I'm close but I have a bug. I am relatively new to 3D rotations and have a basic understanding of what is going on.

``````public static Matrix4D Rotate(Vector3D u, Vector3D v)
{
double angle = Acos(u.Dot(v));
Vector3D axis = u.Cross(v);

double c = Cos(angle);
double s = Sin(angle);
double t = 1 - c;

return  new Matrix4D(new double [,]
{
{ c + Pow(axis.X, 2) * t,  axis.X * axis.Y * t -axis.Z * s, axis.X * axis.Z * t + axis.Y * s, 0 },
{ axis.Y * axis.X * t + axis.Z * s, c + Pow(axis.Y, 2) * t, axis.Y * axis.Z * t - axis.X * s, 0 },
{ axis.Z * axis.X * t - axis.Y * s, axis.Z * axis.Y * t + axis.X * s, c + Pow(axis.Z, 2) * t, 0 },
{ 0, 0, 0, 1 }
});
}
```
```

The above code is the algorithm for the matrix rotation. When I test the algorithm with unit vectors I get the following:

``````Matrix4D rotationMatrix = Matrix4D.Rotate(new Vector3D(1, 0, 0), new Vector3D(0, 0, 1));

Vector4D vectorToRotate = new Vector4D(1,0,0,0);

Vector4D result = rotationMatrix * vectorToRotate;

//Result
X = 0.0000000000000000612;
Y = 0;
Z = 1;
Length = 1;
```
```

With a 90 degree rotation I find it works almost perfectly. Now lets look at a 45 degree rotation:

``````Matrix4D rotationMatrix = Matrix4D.Rotate(new Vector3D(1, 0, 0), new Vector3D(1, 0, 1).Normalize());

Vector4D vectorToRotate = new Vector4D(1,0,0,0);

Vector4D result = rotationMatrix * vectorToRotate;

//Result
X = .70710678118654746;
Y = 0;
Z = .5;
Length = 0.8660254037844386;
```
```

When we take the atan(.5/.707) we find that we have a 35.28 degree rotation instead of a 45 degree rotation. Also the length of the vector is changing from 1 to .866. Does anyone have any tips on what I am doing wrong?

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